Question

If 5 $tan\theta =4,$ then value of $\frac{5sin\theta -3cos\theta }{5sin\theta +2cos\theta }$ is

• A. $\frac{1}{3}$
• B. $\frac{1}{6}$
• C. $\frac{4}{5}$
• D. $\frac{2}{3}$

Answer 1

The correct option is B $\frac{1}{6}$

$Given5tan\theta =4or\frac{sin\theta }{cos\theta }=\frac{4}{5}\therefore sin\theta =\frac{4}{5}cos\theta Thegiventrigonometricexpressionis\to \frac{5sin\theta -3cos\theta }{5sin\theta +2cos\theta }(Substitutingsin\theta =\frac{4}{5}cos\theta )=\frac{5\times \frac{4}{5}cos\theta -3cos\theta }{5\times \frac{4}{5}cos\theta +2cos\theta }=\frac{4-3}{4+2}=\frac{1}{6}$